Recent Results with Regard to SVD-Based Metrics on Rigid-Body Displacements

We present recent results with regard to projective rigid-body displacement metrics. First, we present a methodology for representing rigid-body displacements in SE(n-1) with hyper dimensional rotations in SO(n). Second, we present the inverse mapping of elements of SO(n) to SE(n-1). Finally, we discuss the use of these mappings to facilitate approximately bi-invariant metrics on SE(n). These metrics have applications in approximate motion synthesis, robot calibration, motion interpolation, and path planning.